Plane Wall Case Research Articles

Characterizing the Effect of Sinusoidal Wall Amplitude on Turbulent Wall Jet Flow Parameters

Abstract The influence of wavy wall amplitude on the turbulent wall jet flow parameters has been investigated experimentally. For the present study, a sinusoidal wavy wall (y=A* sin(ωx)) has been used where “A=Amp/a” is the amplitude, which is normalized by the nozzle height “a.” The amplitude of the wavy wall is varied as 0.2, 0.4, and 0.6, and the results are compared with the results of plane wall jet. The constant temperature anemometer (CTA) has been used for the measurement of flow by using a transverse mechanism. The results for the mean velocity profile, turbulent intensity, and power spectral density are plotted at the crest and trough separately for more clear discussions. From the velocity profile, it is noticed that the formation of self-similar profile is delayed as the amplitude increases from 0.2 to 0.6, which means flow takes longer time to develop. There is an increase in the local maximum streamwise velocity Umax at crests for increasing amplitude. At the first crest, the rise in Umax is maximum, i.e., Umax is increased by 26%, 37%, and 60% for the amplitudes 0.2, 0.4, and 0.6, respectively, with respect to the plane wall case. In the near flow field, the turbulent intensity also becomes larger for the higher amplitude, which shows higher intermixing of fluid within the jet. This paper also produces the benchmark results which can be used for the validation of the numerical model dealing with the turbulent wall jet flowing over a wavy surface.

Effect of frequency of the wavy wall on turbulent wall jet heat transfer characteristics

The thermal and hydraulic characteristics of a sinusoidal wavy wall are studied numerically to increase the heat transfer rate of the turbulent wall jet. To do so, the sinusoidal profile (y=A∗sin(ωNx)) is used for the wavy wall, where ωN=2πN/L is the frequency with suffix N denoting the number of cycles for the given length L and A is the amplitude. The amplitude “A” is varied from 0 to 0.8a and ωN is changed from ω4 to ω12, to find out the optimum amplitude and frequency for which the heat transfer rate is maximum. The low Reynolds number two equations RNG k−ϵ model is used for the detailed study and to understand the impact of a re-circulation zone on the heat transfer rate. The inlet velocity is uniform and equals to 10.95 m/s for all the cases to achieve the inlet Reynolds number 15000 for a 20 mm nozzle height. At the inlet, jet is heated to a temperature of 330 K and the wavy wall on which the jet flows is provided an isothermal condition with 300 K temperature. With these conditions, the results for streamwise maximum velocity decay, skin friction coefficient, re-circulation area and local Nusselt number have been compared for different amplitudes and frequencies of the wavy wall. From the results, it has been observed that with the increasing amplitude and frequency the Umax increases, the area of re-circulation zone increases and the thermal potential core decreases. For the wavy wall amplitude A = 0.8 and frequency ω12, the peak of Umax is 170% more than the plane wall jet, the area covered by re-circulation zone is 58.2% of the total area and the thermal potential core reduces to X=3.7 which is about 50% of the plane wall jet. The local Nusselt number also increases with the increasing amplitude and frequency in the near field, but in the far field it starts decreasing as the re-circulation effect dominates there. For the wavy wall, the maximum increase in heat transfer rate is 23.23% with respect to the plane wall case.

Surface conductivity effects during shock wave reflection off curved surfaces

Previous work has shown that heat transfer into a plane conducting surface affects shock wave reflection properties. In the more complex reflection case of a curved surface the situation would be different because of the increased number of reflection patterns, with a rapid change in reflection geometry as the wave propagates up the surface. Test pieces of different thermal conductivities (0.19 W/mK and 401 W/mK) and hydraulically smooth surfaces are used on both convex and concave cylindrical surfaces. The test pieces are placed in identical positions on either side of a plane of symmetry and at the same incident angles in a shock tube. Tests are performed at incident shock Mach numbers of 1.22< M <1.5 and imaged using high-speed shadowgraph photography. The images are analyzed both quantitatively through reflection angle measurements and qualitatively by searching for asymmetry. Both the qualitative and quantitative measurements clearly indicate that the thermal conductivity of the surface affects the reflection patterns due to the complex transient thermal environment. Asymmetry in the reflection patterns is found at all Mach numbers. In contrast to the plane wall case the lack of theory limits comparison, where in that case it was shown that the lower the thermal conductivity the closer the experimental results approached the ideal adiabatic case. Similar comparisons in the relationship of reflection types between different materials are found in the current case. The findings could be refined by using higher imaging frame rates and spatial resolution, and sophisticated numerical modeling.

Role of a Sinusoidal Wavy Surface in Enhancement of Heat Transfer Using Turbulent Dual Jet

Abstract In this paper, the role of sinusoidal wavy surface in enhancing the heat transfer is numerically studied. The heat transfer characteristics are studied for two thermal boundary conditions of the wavy wall. To assess the effect of wavy wall, the amplitude is varied between 0.1 and 0.7 and number of cycle from 4 to 12 at an interval of 0.1 and 1, respectively. In order to see the effect of offset ratio, it is varied between 3 and 15 at an interval of 2. The Reynolds number (Re) and Prandtl number (Pr) are set to 15, 000 and 0.71, respectively, for all the numerical simulations. It is found that the maximum average Nusselt number (Nuavg) depends not only on the amplitude and number of cycle but also on the offset ratio. Overall, 23.27% in maximum heat transfer enhancement is achieved with reference to the plane wall surface. An approximately linear decrement in maximum Nuavg is observed when offset ratio increases. The results indicate that Nuavg increases with an increase in the amplitude of sinusoidal wavy surface up to N = 8 and almost follows the linear trend up to N = 7. It is also found that Nux is always on the higher side as compared to the corresponding case of a plane wall surface when N = 4, irrespective of the offset ratio. With an increase in N, Nux fluctuates about the result of plane wall surface after the initial increase because of the obstruction. The amplitude of the fluctuation increases with an increase in the number of cycle N, which indicates that fluid accelerates and decelerates gradually owing to the presence of trough and crest. Also, it is worth noticing that for some cases, there is a decrease in the heat transfer rate as compared to the plane wall case. Therefore, it is concluded that the increase in the surface area does not necessarily result in an increase in the heat transfer rate.

Turbulent drag reduction over curved walls

This work studies the effects of skin-friction drag reduction in a turbulent flow over a curved wall, with a view to understanding the relationship between the reduction of friction and changes to the total aerodynamic drag. Direct numerical simulations (DNS) are carried out for an incompressible turbulent flow in a channel where one wall has a small bump; two bump geometries are considered, that produce mildly separated and attached flows. Friction drag reduction is achieved by applying streamwise-travelling waves of spanwise velocity (StTW). The local friction reduction produced by the StTW is found to vary along the curved wall, leading to a global friction reduction that, for the cases studied, is up to 10\% larger than that obtained in the plane-wall case. Moreover, the modified skin friction induces non-negligible changes of pressure drag, which is favorably affected by StTW and globally reduces by up to 10\%. The net power saving, accounting for the power required to create the StTW, is positive and, for the cases studied, is one half larger than the net saving of the planar case. The study suggests that reducing friction at the surface of a body of complex shape induces further effects, a simplistic evaluation of which might lead to underestimating the total drag reduction.

Effect of wavy wall surface on flow structure and thermal characteristics of a turbulent dual jet comprising of a wall jet and an offset jet

The fluid flow and thermal characteristics of the dual jet are explored numerically. The dual jet is considered with a wavy wall surface having various amplitudes varying between 0.1 and 0.7 with a fixed number of cycles equal to 10. The offset ratio is also varied from 3 to 15 with an interval of 2. The Reynolds number and Prandtl number are set to 15,000 and 0.71, respectively. The Semi Implicit Method for Pressure Linked Equation algorithm is utilised to link the pressure to the velocity. To solve the set of linear algebraic equations Strongly Implicit procedure solver is used. The heat transfer characteristics of the wavy wall surface were studied for two cases: (1) isothermal bottom wall and (2) adiabatic bottom wall. It is found that the wavy wall affects the flow field and heat transfer characteristics drastically. The minimum pressure inside the domain is not found to occur at the vortex centre for all the offset ratios, which is the case of a dual jet with a plane wall. Results also reveal that as the amplitude of the wavy surface increases both local Nusselt number and local heat flux increase near the exit of the nozzle for each offset ratio. Further, it is also noticed that the average Nusselt number increases up to amplitude A = 0.5. Thereafter, it decreases with further increase in the amplitude of the wavy surface. It is found that the wavy surface increases the average Nusselt number by a maximum of 17.6% as compared to the plane wall case.

Enhancement of heat transfer using turbulent wall jet

Enhancement of heat transfer is very important in many engineering applications. The present study explores one of such possibilities by increasing the surface area of a plane wall. The effect of wavy wall on thermal and flow characteristics of a turbulent wall jet is studied in detail. The amplitude of the wavy surface is varied between 0.1 and 0.7 with an interval of 0.1. The Reynolds number is set to 15,000. The Reynolds averaged Navier Stokes equations are solved using the finite volume approach. The semi-implicit pressure linked equation algorithm is used to couple the pressure and velocity. A new scale, other than the traditional outer scaling, is defined for carrying out the self-similar behavior of the flow. Unlike the plane wall case, the self-similar characteristic is obtained at the respective crests and the troughs. However, it is also noticed that the two characteristics differ significantly with each other. Even, these characteristics are found to differ with each other for different amplitudes. The minimum pressure near the nozzle decreases as the amplitude increases and it is noted to be equal to −0.541 for the highest amplitude, i.e. A = 0.7. It is observed that the strength of convection near the exit of the jet is very high, and it decreases in the downstream direction. This increase in convection augments heat transfer by almost 10% as compared to the plane wall case. Based on the results, a quartic curve is fit for the average Nusselt number with a 99.75% goodness of fit. It is expected that the present study opens a new line in designing a proper cooling system.

Numerical study to enhance the heat transfer using sinusoidal wavy surface for turbulent wall jet

To achieve higher heat transfer rate for cooling by air jet impingement is the most essential goal of the modern era. The aim of this article is to enhance the heat transfer rate significantly by using the sinusoidal wavy surface in a turbulent wall jet. A comprehensive numerical study is carried out to examine the complex behavior of turbulent wall jet flowing tangentially to the wavy surface. To explore all the possibilities associated with the wavy surface, the various number of cycles and amplitudes are considered; the number of cycle (n) is varied between 4 and 12 and the amplitude (A) is changed from 0.1 to 0.7. The results indicate that the local Nusselt number, local heat flux and Umax increase near the exit of the nozzle, while Pmin decreases when the amplitude of the wavy surface increases. Although these parameters increase near the jet exit; but the fate of these parameters are highly dependent on the number of cycle (n) and the amplitude of the wavy surface (A) in the downstream direction. Accordingly, a maximum increase of 14.43% of heat transfer rate is observed for n = 7 and A = 0.7. Also, the self-similar behavior shows different trends as compared to the plane wall case which is discussed in detail.

Fluid flow analysis of a turbulent offset jet impinging on a wavy wall surface

The fluid flow characteristics of a turbulent offset jet impinging on a wavy wall surface has been investigated numerically. Two-dimensional Reynolds-averaged Navier–Stokes (RANS) equations are solved by the finite volume method. In the governing differential equations, the convective and diffusive terms are discretized by the power law upwind scheme and second-order central difference, respectively. The semi-implicit method for pressure linked equation algorithm is utilized to link the pressure to the velocity. The offset ratio is set to 7.0 and the Reynolds number is fixed to 15,000. The width of the jet is taken as the characteristic length. The amplitude of the wavy wall surface is varied from 0.1 to 0.7 with an interval of 0.1 and the number of cycle is fixed to 10. The results of fluid flow and turbulent characteristics of the offset jet are presented in the form of contours of streamline, velocity vector, turbulent kinetic energy, dissipation rate, pressure, and Reynolds shear stress. The variation in integral constant of momentum flux, wall shear stress, and pressure along the wall is presented and also compared. The decay in the maximum streamwise velocity in the downstream direction and jet half-width along the streamwise direction are also presented and discussed. The wavy surface introduces some remarkable features, which are not present in a normal plane wall case. These features have been discussed in detail.

Photodetachment spectrum of hydrogen negative ion near a spherical surface

The semi-classical closed orbit theory is applied to study photodetachment of H− near an elastic spherical surface for a z-polarized laser light. It is assumed that similar to the outgoing detached-electron waves from the source, waves propagate from an image of the source behind the surface. We then calculate the classical action for those trajectories that are perpendicular to the surface. The spherical effects in total photodetachment cross section are controlled by curvature κ of the surface. For zero curvature, our results match with the plane wall case while for a large curvature the results become the asymptotic value of the cross section recently published.

The investigation of spherical effects on the photodetached electron spectra

A theoretical imaging method is used to study the induced effects of a spherical surface on the photodetached electron spectra of a mono-atomic negative ion (H−). Analytical formulas are derived for the detached electron flux and the total photodetachment cross section. The radius of the spherical surface strongly affects the spectra of the flux as well as the cross section. The analysis of the spectra reveals that the curvature of the surface controls the oscillations in the spectra, and the plane wall case reported in Afaq and Du (2007 J. Phys. B: At. Mol. Opt. Phys. 40 1309) is a special case of the spherical surface.

Shock wave interaction with convex circular cylindrical surfaces

The reflection of shock waves off cylindrical surfaces of different radii is examined with the help of time-resolved flow visualization. The primary diagnostic is a newly developed technique based on the tracking of deliberately introduced small perturbations in the flow. The main focus of the investigation is to determine at which position the shock wave receives information about the shape of the wall that it reflects off. In the pseudo-steady shock reflection off a plane wall, it is commonly accepted that the reflection changes from regular to irregular as soon as sonic signals generated behind the reflection point catch up with the reflection point, and the common interpretation is that this corresponds to the transition from regular to Mach reflection (the so-called sonic criterion). The results obtained here for convex circular surfaces show that this ‘catch-up’ condition occurs at wall angles considerably higher than in the plane wall case, while a visible Mach stem occurs only further along the surface at wall angles distinctively lower than those for plane walls. Tests are also conducted on a surface where a cylindrical portion is followed by a fixed angle plane section. The Mach numbers are chosen to be on either side of the plane wall transition condition so as to examine the adjustment from reflection on the cylindrical portion to that on the plane wall. These tests confirm that the wall angle at which sonic ‘catch-up’ to the reflection point occurs on the cylindrical surface is much higher than the corresponding wall angle predicted by the sonic criterion for a plane wall. While the transition from regular to irregular reflection is not the main concern of this contribution, the present results show that the transition criteria developed for steady and pseudo-steady flows are only of limited use in the fully unsteady flows such as the one investigated here.

Intermittent turbulence in a pulsating pipe flow

Numerical simulations of the pulsating flow in a pipe of circular cross-section characterized by small imperfections are carried out to determine the conditions leading to the appearance of turbulence. The results show that in the oscillatory case (no steady velocity component of the basic flow), the critical value of the Reynolds number Rδ depends on the Womersley parameter α and, in particular, Rδ increases as α decreases. The critical value of Rδ of the plane wall case is recovered when α is larger than about 10. For moderate values of the Reynolds numbers but larger than the critical one, turbulence appears around flow reversal and breaks the symmetry of the flow, originating a steady velocity component. Moreover, turbulence is not present throughout the whole cycle and there are phases during which the flow relaminarizes. The presence of a steady pressure gradient tends to destabilize the flow and this destabilizing effect becomes larger as the steady velocity component is increased. When turbulence is present, its dynamics is similar to that of the steady case and a log-law layer can be identified both in the oscillatory and the pulsating case.

Laminar jet impingement on an indented wall

The Navier-Stokes equations are solved numerically to study the problems of laminar, axisymmetric jet impinging normally on an indented wall. The results obtained for three different wall geometries and Reynolds number range upto 25 are compared with those for the impingement on a plane wall to study the influence of indentation. The overall flow picture remains similar to the plane wall case qualitatively but the wall shear stress and pressure distribution get altered in the indented region.

The three dimensional turbulent corner wall jet

SummaryExperiments are reported of the self-preserving turbulent corner wall jet formed by directing a jet of air parallel to the line of intersection of two walls abutting at right angles. Self preserving profiles of the mean and turbulent flow are established by approximately 50 jet diameters downstream. Like the three-dimensional wall jet on a plane-wall surface there is evidence of a significant secondary flow induced by vortex line bending, though its magnitude is smaller than in the plane-wall case.

Calculation of magnetic domain wall bowing and eddy current losses in an infinite sheet of bar-like domains

An analytic solution has been obtained for the magnetic field distribution and eddy current losses associated with an infinite array of regularly spaced 180° domain walls which are allowed to bow during their motion. Wall motion was constrained to satisfy a sinusoidal total flux boundary condition. The field solution was solved self-consistently with the domain wall equation of motion. Calculated losses were always lowered relative to the plane wall case. Difficulties were encountered in the numerical iteration scheme as the degree of bowing increased. Using an approximation for the high bowing case, a physical instability occurred before bowing became too severe.

Long Waves on a Film Flow of a Viscous Fluid down an Inclined Uneven Wall

This paper deals With long nonlinear waves on a film flow of a viscous fluid down an inclined uneven wall. A system of equations for the free surface is derived to the first order accuracy of the shallow water parameter. When the derivative expansion method is applied to this system, it is shown that a fluctuation on the nonparallel basic steady flow is perturbed from that on the corresponding steady flow down a plane wall inclined at the same angle owing to the ununiformity of the basic flow. The linear stability of the basic flow is identical with that for the plane wall case. Near the upper branch of the neutral curve, the flow on the uneven wall is found to be supercritically stable and long waves of equilibrium amplitude are complicatedly perturbed from the corresponding waves for the plane wall case.

Long Waves on Film Flow of Viscous Fluid down the Surface of a Vertical Cylinder

This paper deals with long waves on a film flow of a viscous fluid down the inner or outer surface of a vertical tube of circular cross-section. A dispersion relation is derived for infinitesimal sinusoidal waves on the basic steady flow. A nonlinear asymptotic equation is also derived for the surface elevation by making use of the method of derivative expansion. It is shown that this equation is reducible to that for the plane wall case by a simple transformation. Hence, any linearly unstable periodic wave, whose wave number is close to the upper branch of the neutral curve, develops into a progressing wave train of finite amplitude.

Transient heat dissipation from storage reservoirs

An analysis of the transient behaviour of internally heated reservoirs or buildings is presented. New solutions for simplified geometrical models, which take account of both fluid heat capacity and convection resistance at the walls, are derived as a significant step towards the solution of the more general problem. The geometrical models considered are: the plane semi-infinite wall in contact with a well-mixed fluid and the spherical cavity in an infinite solid. Solutions are presented for both time dependent and time independent heat input rates. Generally valid graphs and tables for the plane wall case with constant heat input rate are given.